Evaluate the following one sided limits: _ x 0^- (1+cosec x) - Vidyadip

Question

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow0^-}(1+\text{cosec }\text{x})$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0^-}(1+\text{cosec }\text{x})$
$=\lim\limits_{\text{x}\rightarrow0^-}1+\text{cosec }(0-\text{h})$
$=\lim\limits_{\text{h}\rightarrow0}\ 1-\text{cosec}\text{ h}$
$=\lim\limits_{\text{h}\rightarrow0}1-\frac{1}{\sin\text{h}}$
$\Rightarrow1-\frac{1}{0}=-\infty$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the domain and range of the following real valued functions:
$\text{f(x)}=\sqrt{\text{x}-3}$

Find the distance between the following pairs of points:
P(1, -1, 0) and Q(2, 1, 2)

In a simultanepous throw of a pair of dice, find the probability of getting,A number greather than 4 on each die.

Find the $12^{th}$ term from the end of the following arithmetic progressions,
$3, 5, 7, 9, ... 201$

Evaluate the following:
$\text{i}^{30}+\text{i}^{40}+\text{i}^{60}$

A die is thrown twice Each time the number appearing on it is recorded Describe the following events:
A = Both numbers are odd.

Find the A.M. between:
(x - y) and (x + y)

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}^2}{\sin\text{x}^2}$

In a single throw of a die describe the following events:
D = Getting a number less than 4

Write the relation in the Roster form. State its domain and range.

$R_8=\{(a, b) / b=a+2, a \in Z, 0<a<5\}$